I find once well seasoned cooking tomatoes or other acidic foods once in a while does basically nothing to the seasoning. Just fry some bacon in it after.
Strangely enough, this is a good reason for preferring cast iron over Teflon! Cast iron is close to indestructible, whereas with PTFE or other non-stick coatings one is constantly worried about scratching.
Other (non-mandatory) egg-in-cast-iron advice: use a stainless steel fish flipper (very thin and flexible). For me, if I want the top a bit more cooked, I do the tbsp water + lid trick to finish it off.
I suspect the goal was to stop the bottom from over cooking (insulate it) and perhaps generate a bit of steam to help with setting the top of the eggs slightly. The goal was perfect sunny-side up eggs as best I recall. Seems like it would work just as well with all steps done in a cast iron pan?
Was the lettuce served with the egg as well, or just discarded? I could see either - as you say, providing just a bit of insulation and moisture to finish cooking the top without overcooking the bottom.
It actually lasts forever, depending how you look at it
That's the main reason I own only cast iron. I like to buy things once and keep them forever. It's really not that much of a pain to use. I've never seasoned or otherwise serviced my cast iron in 8 years of use. It's heavy and a bit more tedious to clean without using soap. But I've never had to throw out or buy another pan, and it feels good to be using something you know will last for the rest of your life.